Wordwind's scathing indictment of the Ailanthus tree prompted me to look it up. I found some interesting facts about it. It was "The Tree That Grew In Brooklyn." It was introduced into this country over two hundred years ago. The reason it is becoming a pest is that it is resistant to diseases, which can also be a virtue. It is dioecious meaning there are male and female trees. (Yes, Virginia, trees do have sex but it is not very exciting)(And forests have climaxes, but it takes them a couple hundred years.) Both sexes have a downside about either flowers or leaves having a bad odor when crushed. There is a dictionary of botanical terms with lots of dandy words to learn.
The one thing I could not find out is how valuable they are for shade. Here is one URL (others can be found by searching "Botany ailanthus").http://www.botanyworld.com/16.di.htm

Ailanthus trees also have the habit of growing more roots than canopy-- so they are able to get a toe hold in, and grow where many things can't --Like cracks in a sidewalk.

the flowers of the male tree smell like burnt starch-- anyone here besides me ever leave some potatoes over a low heat with almost no water in the pot, to steam them-- and get busy with something and forget them? or has any one else burnt rice (no, i an not the best cook-- and yes i have blown up my pressure cooker) If so, you know that horrid burnt starch smell.. just like Ailanthus tree flowers.

the fruit, smells like vomit. there is no nice way to say it, and you don't ever want to be around it. books are nice "a mildly offensive odor"-- let me tell you, being around an Ailanthus tree is enough to make you sick!

but, when they are mature (about 50 years old or so) they have a beautiful shape, and give lovely shade.. (except when flowering or fruiting!)